Đáp án:
Giải thích các bước giải:
\(a,\\ x^{2}.\left (5x^{3}-x-\dfrac{1}{2} \right )\\ =5x^{5}-x^{3}-\dfrac{1}{2}x^{2}\\ b,\\ (3xy-x^{2}+y).\dfrac{2}{3}x^{2}y\\ =2x^{3}y^{2}-\dfrac{2}{3}x^{4}y+\dfrac{2}{3}x^{2}y^{2}\\ c,\\ (4x^{3}-5xy+2x).\left (\dfrac{-1}{2}xy \right )\\ =(-2x^{4}y)+\dfrac{5}{2}x^{2}y^{2}-x^{2}y\\ d,\\ (x-2).(x^{2}+3x-5)\\ =x.(x^{2}+3x-5)-2.(x^{2}+3x-5)\\ =(x^{3}+3x^{2}-5x)-(2x^{2}+6x-10)\\ =x^{3}+3x^{2}-5x-2x^{2}-6x+10\\ =x^{3}+(3x^{2}-2x^{2})+(-5x-6x)+10\\ =x^{3}+x^{2}-11x+10\\ e,\\ (3x-2y).(x^{2}+xy-1)\\ =3x.(x^{2}+xy-1)-2y.(x^{2}+xy-1)\\ =(3x^{3}+3x^{2}y-3x)-(2x^{2}y+2xy^{2}-2y)\\ =3x^{3}+3x^{2}y-3x-2x^{2}y-2xy^{2}+2y\\ =3x^{3}+(3x^{2}y-2x^{2}y)-3x-2xy^{2}+2y\\ =3x^{3}+x^{2}y-3x-2xy^{2}+2y\\ f,\\ (x-2)(x+2)(x+3)\\ =(x^{2}-4)(x+3)\\ =x^{2}.(x+3)-4.(x+3)\\ =x^{3}+3x^{2}-4x-12\\ g,\\ 4(x-1)(x+5)-(x+2)(x+5)-3(x-1)(x+2)\\ =4(x-1)(x+5)-(x+2)(x+5)-4(x-1)(x+2)+(x-1)(x+2)\\ =\left [4(x-1)(x+5)-4(x-1)(x+2) \right ]-\left [(x+2)(x+5)-(x-1)(x+2) \right ]\\ =4(x-1)(x+5-x-2)-(x+2)(x+5-x+1)\\ =(4x-4).3-(x+2).6\\ =12x-12-6x-12\\ =(12x-6x)+(-12-12)\\ =6x-24\)
chúc bạn học tốt!
